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We investigate the recurrence properties of the time series of quantummechanical expectation values, in terms of two representative models for asingle-mode radiation field interacting with a nonlinear medium. Fromrecurrence-time distributions, return maps and recurrence plots, we concludethat the dynamics of appropriate observables pertaining to the field can varyfrom quasiperiodicity to hyperbolicity, depending on the extent of thenonlinearity and of the departure from coherence of the initial state of thefield. We establish that, in a simple bipartite model in which the field iseffectively an open quantum system, a decaying exponential recurrence-timedistribution, characteristic of a hyperbolic dynamical system, is associatedwith chaotic temporal evolution as characterized by a positive Liapunovexponent.

Recurrence properties of quantum observables in wave packet dynamics